## Classification of trisections and the Generalized Property R Conjecture

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- by Jeffrey Meier, Trent Schirmer and Alexander Zupan PDF
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**144**(2016), 4983-4997 Request permission

## Abstract:

We show that the members of a large class of unbalanced four-manifold trisections are standard, and we present a family of trisections that is likely to include non-standard trisections of the four-sphere. As an application, we prove a stable version of the Generalized Property R Conjecture for $c$–component links with tunnel number at most $c$.## References

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## Additional Information

**Jeffrey Meier**- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47408
- MR Author ID: 849257
- Email: jlmeier@indiana.edu
**Trent Schirmer**- Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
- Email: trent.schirmer@okstate.edu
**Alexander Zupan**- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
- Address at time of publication: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska, 68588
- MR Author ID: 863648
- Email: zupan@unl.edu
- Received by editor(s): March 30, 2015
- Received by editor(s) in revised form: August 6, 2015, and January 14, 2016
- Published electronically: May 24, 2016
- Communicated by: Martin Scharlemann
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**144**(2016), 4983-4997 - MSC (2010): Primary 57M25, 57M99, 57Q25
- DOI: https://doi.org/10.1090/proc/13105
- MathSciNet review: 3544545